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SFB 649 Discussion Papers, HU Berlin >
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http://hdl.handle.net/10419/56623
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| Title: | | A Donsker theorem for Lévy measures  |
| Authors: | | Nickl, Richard Reiß, Markus |
| Issue Date: | | 2012 |
| Series/Report no.: | | SFB 649 discussion paper 2012-003 |
| Abstract: | | Given n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes. |
| Subjects: | | uniform central limit theorem nonlinear inverse problem smoothed empirical processes pseudo-differential operators jump measure |
| JEL: | | C14 C22 |
| Document Type: | | Working Paper |
| Appears in Collections: | | SFB 649 Discussion Papers, HU Berlin
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